ComplexExpand[expr] expands expr assuming that all variables are real.
ComplexExpand[expr, , , ... ] expands expr assuming that variables matching any of the are complex.
Example: ComplexExpand[Sin[x + I y]]. The variables given in the second argument of ComplexExpand can be patterns. Example: ComplexExpand[Sin[x], x]. See The Mathematica Book on the web: Section 1.4.5 and Section 3.3.8. See also: GaussianIntegers, TrigToExp, ExpToTrig, TrigExpand.
ComplexExpand[expr] expands expr assuming that all variables are real. 
, 
, ... 
] expands expr assuming that variables matching any of the 
are complex. 
. 
. 